In a food processor with a knife blade attached, puree the beans and lime juice until smooth. Transfer to a medium bowl.
In the same processor, place the cilantro, onions, salt and jalapeno, and pulse until juicy and thick. With a spoon, scoop the avocado from the peel into the bowl with the beans. Mash with a fork until the mixture is blended, with some chunks remaining.
Cut each tomato crosswise in half. Squeeze the halves to remove the seeds and juice. Coarsely chop the tomatoes. Stir the onion mixture and tomatoes into the avocado mixture until blended. If you prefer a little more zip, stir in additional lime juice to taste. Garnish with basil, if you like. Serve with chips and vegetables.